W varies directly as r cubed and inversely as s. If w=24 when r= 4 and s= 8, find out when w= 81 and s= 27?

Answer:

b. DC = 29 and DE = 44.5

Step-by-step explanation:

Given:

AB = 29

BD = 89

Required:

DC and DE

Solution:

Recall: diagonals of a parallelogram bisect each other into equal segments. Also, pairs of parallel sides are equal.

✔️DC = AB = 29 (parallel sides of parallelogram)

DC = 29

✔️DE = ½(DB) (diagonals bisect each other into equal parts)

Substitute

DE = ½(89)

DE = 44.5

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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The statement that proves that ∠3 ≅ ∠7 is: C. If two parallel lines are cut by a transversal, the corresponding angles are congruent.

If two angles lie on separate parallel lines that are crossed by a transversal and share relative corner, the angles are corresponding angles, and according to the corresponding angles theorem, both angles are congruent to each other.

Angles 3 and 7 both lie on relative corner on each parallel lines that are crossed by the transversal, therefore, both are corresponding angles

Applying the corresponding angles theorem, both angles can be proven to be congruent to each other.

Therefore, the right answer is: C. If two parallel lines are cut by a transversal, the corresponding angles are congruent.

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Hey!

For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)

This way, it will be able to graph and get the answers quicker!

The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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The first equation describes the linear graph with a positive slope of 2 and the second equation describes the linear graph with a negative slope of -3. The piecewise-defined function is able to describe the graph perfectly by combining these two equations.

A piecewise-defined function is a function that is defined by multiple expressions, each of which is applicable to a certain range of values. It is common for piecewise-defined functions to be used to represent discontinuous functions, since each of the expressions can be used to define the behavior of the function in different intervals.

The given graph of a piecewise-defined function is defined by two distinct equations. The first equation is y = 2x + 3, which is valid for all x values less than or equal to 1. This equation describes the linear graph with a positive slope of 2 that is shown in the graph. The second equation is y = -3x + 9, which is valid for all x values greater than 1. This equation describes the linear graph with a negative slope of -3 that is shown in the graph.

The piecewise-defined function can be written as f(x) = {2x + 3, x ≤ 1; -3x + 9, x > 1}. This function is defined for all x values and it describes the graph shown above perfectly. The domain of the function is all real numbers, while the range is all real numbers greater than or equal to 3.

The piecewise-defined function is a combination of two linear equations that are valid for different x values. The two equations are joined together at the point (1, 5), which is the point of intersection between the two graphs.

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Answer:

0.42

Step-by-step explanation:

To solve the problem, we need to add the probability of picking a club to the probability of picking a face card, and then subtract the probability of picking a club that is also a face card (because we would have counted it twice).

There are 13 clubs in a standard deck, so the probability of picking a club is 13/52 or 0.25.

There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck, so the probability of picking a face card is 12/52 or 0.23.

However, there are 3 cards that are both clubs and face cards (the jack of clubs, queen of clubs, and king of clubs), so we need to subtract the probability of picking one of those cards. There are 3 of them out of 52 total cards, so the probability of picking a club that is also a face card is 3/52 or 0.06.

Therefore, the probability of picking a club OR a face card is:

0.25 + 0.23 - 0.06 = 0.42 (rounded to two decimal places).

So the answer is 0.42.

Answer:

Line segment AD

\(AD = \sqrt{(c-0)^{2}+(d-0)^{2}}\)

\(AD = \sqrt{c^{2}+d^{2}}\)

Line segment BC

\(BC = \sqrt{[(b+c)-b]^{2}+(d-0)^{2}}\)

\(BC = \sqrt{c^{2}+d^{2}}\)

Line segment AB

\(AB = \sqrt{(b-0)^{2}+(0-0)^{2}}\)

\(AB = \sqrt{b^{2}+0^{2}}\)

\(AB = b\)

Line segment CD

\(CD = \sqrt{[c-(b+c)]^{2}+(d-d)^{2}}\)

\(CD = \sqrt{b^{2}+0^{2}}\)

\(CD = b\)

Step-by-step explanation:

We defined the length of each side by the Equation of the Line Segment, which is a particular case of the Pythagorean Theorem. Let \(A(x,y) = (0,0)\), \(B(x,y) = (b,0)\), \(C(x,y) = (b+c, d)\) and \(D(x,y) = (c,d)\), we construct the equations below:

Line segment AD

\(AD = \sqrt{(c-0)^{2}+(d-0)^{2}}\)

\(AD = \sqrt{c^{2}+d^{2}}\)

Line segment BC

\(BC = \sqrt{[(b+c)-b]^{2}+(d-0)^{2}}\)

\(BC = \sqrt{c^{2}+d^{2}}\)

Line segment AB

\(AB = \sqrt{(b-0)^{2}+(0-0)^{2}}\)

\(AB = \sqrt{b^{2}+0^{2}}\)

\(AB = b\)

Line segment CD

\(CD = \sqrt{[c-(b+c)]^{2}+(d-d)^{2}}\)

\(CD = \sqrt{b^{2}+0^{2}}\)

\(CD = b\)

Answer:

I think it's number two

Answer:

A, first one

Step-by-step explanation:

Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;

$78,000

An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.

The annual salary of Winston as an accountant = $60,000

The amount Winston's financial asset generates = $4,000 per year

The cost of running the business = $8,000

The amount Winston earns as revenue = $150,000

Therefore;

Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000

The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business

The cost of running the business = $8,000

The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost

The total cost = $60,000 + $4,000 + $8,000 = $72,000

The economic profit = The total revenue - The total cost

Therefore;

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1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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Actually, when you solve a sytem of linear equations, it doesn't matter which equation you choose, the solutions will be the same.

Answer:

A

Step-by-step explanation:

Because if you subtract A from A it gets rid of A leaving only B left.

Answer:

y - 5 = 3(x - 4)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

Step-by-step explanation:

Step 1: Define

Slope m = 3

Point (4, 5)

Step 2: Write equation

Point-Slope Form:   y - 5 = 3(x - 4)

Answer:

D

Step-by-step explanation:

2.33 I think

The critical value that corresponds to a 91% confidence level is 1.7

'Critical value is a cut-off value that is used to mark the start of a region where the test statistic, obtained in hypothesis testing, is unlikely to fall in. In hypothesis testing, the critical value is compared with the obtained test statistic to determine whether the null hypothesis has to be rejected or not.'

According to the given problem,

Confidence level = 91%

Now, α = ( 100 - 91 ) %

             = 9%

             = 0.09

Area of each tail = \(\frac{0.09}{2}\)

                             = 0.045

Area in the middle = 1 - 0.045

                               = 0.955

Now, if we look up this area on the z-table, the critical value will come as 1.6954, which is nearly equal to 1.7.

Hence, we can conclude, the critical value is 1.7.

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Answer:

Center ( -8, 1 )

Radius ( 13 )

Therefore, when h = 6 and j = 5, the value of hj - h² is -6.

Arithmetic operations are basic mathematical operations that involve manipulating numbers to perform calculations. There are four main arithmetic operations:

Addition: Adding two or more numbers together. The symbol used to represent addition is "+", and the result is called the sum.

Subtraction: Subtracting one number from another. The symbol used to represent subtraction is "-", and the result is called the difference.

Multiplication: Multiplying two or more numbers together. The symbol used to represent multiplication is "×" or "*", and the result is called the product.

Division: Dividing one number by another. The symbol used to represent division is "÷" or "/", and the result is called the quotient.

These operations can be combined to perform more complex calculations. Additionally, there are other arithmetic operations, such as exponentiation (raising a number to a power) and finding roots, which involve using arithmetic principles.

by the question.

To evaluate the expression hj - h² for h = 6 and j = 5, we simply substitute these values into the expression and perform the arithmetic operations:

hj - h² = (6)(5) - 6²

= 30 - 36

= -6

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Answer:

x=8, y=4

Step-by-step explanation:

I solved it using the substitution method, but any works really.

x+y=12

x-2y=0

x=12-y

Plug in given value of x:

12-y-2y=0

12-3y=0

-3y=-12

y=4

Plug in given value of y into first equation:

x+y=12

x+4=12

x=12-4

x=8

We can also do this using the Gauss method:

x+y=12 (Multiply this equation by -1)

x-2y=0

-x-y=-12 (Add both equations together)

x-2y=0

x-x-2y-y=-12+0 (Cancel out x and -x)

-3y=-12

y=4

Plug in given value of y:

x+y=12

x+4=12

x=8

Hope this helps!

a. We can start by factoring out the greatest common factor of the three terms, which is 2: 2(x² - 3x - 10)

b. 2x² - 6x - 20 can be factorized as 2(x - 5)(x + 2).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

a. To fill in the gaps, we need to factorise the quadratic expression 2x² - 6x - 20. We can start by factoring out the greatest common factor of the three terms, which is 2:

2(x² - 3x - 10)

b. To factorise 2x² - 6x - 20 into a(x+b)(x+c), we need to find values for a, b, and c such that:

a(x+b)(x+c) = 2x² - 6x - 20

Expanding the right-hand side of the equation gives:

a(x² + bx + cx + bc) = 2x² - 6x - 20

We can simplify the left-hand side by grouping the "x" terms together:

a(x² + (b+c)x + bc) = 2x² - 6x - 20

Since this equation must hold for all values of x, we can equate the coefficients of x², x, and the constant term separately:

Coefficient of x²: a = 2

Coefficient of x: a(b+c) = -6

Constant term: abc = -20

From the first equation, we know that a = 2. Substituting this into the second equation gives:

2(b+c) = -6

b + c = -3

To solve for b and c, we can use the third equation:

2bc = -20

We need to find two values of b and c that multiply to -10 (since 2 is already determined) and add up to -3. One possible pair of values is -5 and 2, since (-5)(2) = -10 and (-5) + 2 = -3. Therefore, we have:

b = -5, c = 2

Substituting these values into the factored form, we get:

2x^2 - 6x - 20 = 2(x - 5)(x + 2)

Therefore, 2x² - 6x - 20 can be factorised as 2(x - 5)(x + 2).

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Answer:

around 9900.6 balls can fit in the room

Step-by-step explanation:

It is true that the line segment AB equals 26

The given parameters are:

AB = x +16

BC = 4x + 11

AC = 77

The two-column proof is as follows:

AC = AB + BC                     Line segment formula

77 = x + 16 + 4x + 11            Substitution property of equation

77 = 5x + 27                        Addition property of equation

5x = 50                               Subtraction property of equation  

x = 10                                    Division property of equation

AB = 10 +16                          Substitution property of equation

AB = 26

Hence, the line segment AB has been proved to equal 26

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Answer:

Step-by-step explanation:

\(v = \sqrt{ {u}^{2} + 2at} \)

when u = 1.6

a = 5.6

t = 2

Substitute the values into the above formula and solve for v

That's

\(v = \sqrt{ {1.6}^{2} + 2(5.6)(2) } \\ = \sqrt{2.56 +2(11.2) } \\ = \sqrt{2.56 + 22.4} \: \: \: \: \: \: \\ = \sqrt{24.96} \\ = 4.99599\)

We have the final answer as

Hope this helps you

The average rate of change of the given equation is -4.

The fundamental principle for determining the average rate of change is one of the fundamental ideas in calculus and is used whenever we desire to describe how quantities change over time.

How do you determine the average rate of change, then?

The average rate of change measures how quickly one function is changing in comparison to another.

Calculating the rate at which the output (y-values) changes in relation to its input is all that is required of it (x-values).

How can the average rate of change be determined?

The slope formula is employed!

\(average = \frac{f(b)-f(a)}{b-a}\).

Average rate of change = \(\frac{f(b)-f(a)}{b-a} = \frac{f(-1)-f(-4)}{-1-(-4)}=\frac{f(-1)-f(-4)}{3}\)

Given f(x) = \(1x^{2} +1x-8\)

\(f(-1) = 1(-1)^{2} +1(-1)-8\) = -8.

\(f(-4) = 1(-4)^{2} + 1(-4)-8\) = 4.

Substituting in the average rate of change we get it as -4.

The average rate of change of the given equation is -4.

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Answer:

y = (1/3)x - (1/3)

(1/3)

Step-by-step explanation:

We can find the slope by subtracting Q points by P points.

(2 - (-1)) / (7 - (-2))

3 / 9

1/3 = slope

To find y intercept we can use the slope and find the difference left

y = (1/3)x

-1 = (1/3)(-2)

-1 = -(2/3)

This is not true

To make it true we must subtract -(1/3)

This means our equation is

y = (1/3)x - (1/3)

The number of years of employment is A. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

The system of equations given is:

x = 4y

x = 8 + 2y

You can solve the system by setting the two expressions for x equal to each other:

4y = 8 + 2y

2y = 8

2y / 2 = 8 / 2

y = 4

Substitute y = 4 into the first equation to solve for x:

x = 4 x 4

= 16

So, Mae (y) has been at the company for 4 years and Nikhil (x) has been at the company for 16 years.

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